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Smooth complete toric threefolds with no nontrivial nef line bundles. (English) Zbl 1141.14313

Summary: We describe all of smooth complete toric threefolds of Picard number \(5\) with no nontrivial nef line bundles, and show that no such examples exist with Picard number less than \(5\).

MSC:

14M25 Toric varieties, Newton polyhedra, Okounkov bodies
14C20 Divisors, linear systems, invertible sheaves
14J30 \(3\)-folds
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